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Algebra is not hard

If I were to tell you that I was taking two apples and three oranges home, you'd know what I mean.

Algebra's the same.

You'd know that if I told you that my friend Geoff (I don't have a friend called Geoff) came home with three more apples and five more oranges, that we would have a fruit party, because we're pathetically hungry.

Using algebra is just the same as having shorthand. Maybe it's not the concept, but it's the shorthand that bothers some people?

I don't know that if algebra is difficult for one person then arithmetic is also difficult, but do let me know if it is this way for you!

All algebra's doing is giving things shorter names so that they can be manipulated more quickly. Perhaps that's where the issues start?

If this therefore confuses you, it may be something deeper.

I'm going to have the letter "r" short for oranges here, as having "o" is too much like zero:

2a + 3r + 3a + 5r = ?

Is it easier if I write it in words?

Two apples, and three oranges, and three more apples and five more oranges, is how many of both?

In real life you'd know to count apples together and oranges together, and even if you do it one by one, I'm struggling to see where the difficulty is in that.

Is the difficulty having symbolic metaphors? (I have to use 🔶 for oranges because Blogger doesn't know about them).

2🍏 + 3🔶 + 3🍏 + 5🔶 = ?

Would one have to count them out to make more sense?

🍏🍏🔶🔶🔶🍏🍏🍏🔶🔶🔶🔶🔶 = ?

That's now just simple rearrangement. Is that somehow easier? So, I move some around and...

🍏🍏🔶🔶🔶🍏🍏🍏🔶🔶🔶🔶🔶 = 🍏🍏🍏🍏🍏🔶🔶🔶🔶🔶🔶🔶🔶

Ta-da!

(I wonder how much all of that costs...)

So I really struggle to understand which bit of algebra is difficult for people. Any thoughts, anyone?

Comments

I'm not sure if anyone is having a problem with this part. I can see how manipulating polynomials, especially the long division, can feel highly unusual to people.

Besides, algebra _is_ hard. ;)The fundamental theorem of algebra remains magical for people until much later, when they learn complex analysis, and they have to just believe it. Proving whether a number is algebraic is still a black art.

Fair enough, Daniil. I was only referring to the substitution and basic algebra that people learn in school the first time they do it. Of course there are harder parts, but I only meant the actual understanding was a letter meant a number that can be indefinite. But fair point nonetheless.

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